Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22576190 | C2 | semidirect |
| 2. C2×#22576166 | C2 | semidirect |
| 4. #31774473 | C2 | semidirect |
| 5. #31774154 | C2 | semidirect |
| 6. #31774142 | C2 | semidirect |
| 7. #31774137 | C2 | semidirect |
| 8. #31774125 | C2 | semidirect |
| 9. #31773940 | C2 | semidirect |
| 10. C2×#22576085 | C2 | semidirect |
| 11. #416×C271 | C2 | semidirect |
| 58. #16864638 | D4 | semidirect |
| 143. C271 | #3063 | semidirect |
| 154. #416 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576190 | 2 |
| C2×#22576166 | 2 |
| #31774475 | 2 |
| #31774473 | 2 |
| #31774154 | 2 |
| #31774142 | 2 |
| #31774137 | 2 |
| #31774125 | 2 |
| #31773940 | 2 |
| C2×#22576085 | 2 |
| #416×C271 | 2 |
| #3063 | 271 |